Premium
Symplectic Dirac Operators on Kähler Manifolds
Author(s) -
Habermann Katharina
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/(sici)1522-2616(200003)211:1<37::aid-mana37>3.0.co;2-r
Subject(s) - symplectic geometry , mathematics , symplectic representation , symplectic manifold , moment map , pure mathematics , symplectic vector space , dirac operator , symplectic matrix , spinor , symplectomorphism , clifford analysis , symplectic group , mathematical physics , algebra over a field
The notion of symplectic spinors over a symplectic manifold was already introduced by B. K ostant in 1974 as a tool in his theory of geometric quantization. We observed that it is possible to define canonical symplectic Dirac operators acting on symplectic spinor fields in a similar way as one knows it from the Dirac operator on Riemannian manifolds. In this paper we study symplectic Dirac operators provided that the underlying manifold is a Kähler manifold with the Kähler form as symplectic structure.